The aim of this proposal is to establish the links between the kinds of measure best suited to the study of the determinants of fertility, and the kinds of measure best suited to fertility projections, and thus to the study of the consequences of fertility. The proposal has three parts. (1) The production and analysis of new measurements. (a) Develop interval-specific progression probabilities for birth cohorts, based on postwar American fertility. these probabilities are the proportions of women in a birth cohort with an Nth birth in period t who have an N+1th birth in period t=i. (b) Produce nuptiality functions for birth cohorts, to complement the existent cohort fertility tables. (c) Project the fertility of currently incomplete cohorts, using assumtions about change in the interval-specific progression probabilities. (d) Analyze the quantum and tempo components of the time series of cohort fertility. (2) Develop the translation algebra required to express risk functions for cohorts, such as the progression probabilities, in terms of their period-specific manifestations. (3) Determine the relationships between characteristics of entry distributions (at the beginning of exposure to risk) and characteristics of exit distributions (survival curves), with special attention to the problems of competing risks and the convolution of stopping time and waiting time. The work may be classified as demographic (statistical and mathematical). It is health related because it is designed to achieve a parsimonious description of reproductive behavior in a form which facilitates the study of both its determinants and its consequences.